Theoretical Limits on Errors and Acquisition Rates in Localizing Switchable Fluorophores

TL;DR

This paper establishes theoretical limits on error rates and acquisition speeds in fluorescence microscopy techniques that localize switchable fluorophores, highlighting fundamental tradeoffs and minimal acquisition times.

Contribution

It introduces a formalism for error rate analysis, derives relationships between error, speed, and processing, and identifies the minimum acquisition time regardless of algorithm efficiency.

Findings

Derived a general relationship between error rates and acquisition speed.

Showed existence of a minimum acquisition time independent of algorithm performance.

Analyzed algorithms inferring molecular positions from overlapping images.

Abstract

A variety of recent imaging techniques are able to beat the diffraction limit in fluorescence microcopy by activating and localizing subsets of the fluorescent molecules in the specimen, and repeating this process until all of the molecules have been imaged. In these techniques there is a tradeoff between speed (activating more molecules per imaging cycle) and error rates (activating more molecules risks producing overlapping images that hide information on molecular positions), and so intelligent image-processing approaches are needed to identify and reject overlapping images. We introduce here a formalism for defining error rates, derive a general relationship between error rates, image acquisition rates, and the performance characteristics of the image processing algorithms, and show that there is a minimum acquisition time irrespective of algorithm performance. We also consider algorithms that can infer molecular positions from images of overlapping blurs, and derive the dependence of the minimimum acquisition time on algorithm performance.